- #1

FaraDazed

- 347

- 2

## Homework Statement

prove using the compound angle identies, proove the following:

[tex]

\frac{sin(A-B)}{cos(A)cos(B)}+\frac{sin(B-C)}{cos(B)cos(C)}+\frac{sin(C-A)}{cos(C)cos(A)}=0

[/tex]

## Homework Equations

n/a

## The Attempt at a Solution

I resolved it to

[tex]

\frac{sin(A)cos(B)-cos(A)sin(B)}{cos(A)cos(B)}+\frac{sin(B)cos(C)-cos(B)sin(C)}{cos(B)cos(C)}+\frac{sin(C)cos(A)-cos(C)sin(A)}{cos(C)cos(A)}=0

[/tex]

And using wolfram alpha I found that the first term resolves to tan(A)-tan(B) and then I can see how it equals zero as all the tans would cancel out.

But I have no idea how each term simplifies to that.

Any help is really appreciated.

thanks.